So currently he has:
Every other weekend, one tea time visit on the week he doesn't have the weekend, 1 week summer holidays and 1 week Xmas.
He wants to have:
Every other weekend, ie Fri-Sun then the next week Weds-Fri, so that would be 4 nights a fortnight. He would also like to be more involved with school.
I am not a legal professional so only answering from what I feel seems fair, reasonable and from my experience as a mum with shared residence and a step mum with step children who have shared residence (all in residence orders done via Courts).
What he is asking for seems reasonable, it all depends on how much it will affect the children, will it be better for them, what they want (dependent on age) and whether their mum is justified in saying no.
I understand their mum has agreed to more holiday contact, so she is obviously not just saying no for no reason at all, maybe she does have genuine concerns that may need to be negotiated / talked about. Why can he only accept 1 more week a year school holidays? Surely he has more than 2 weeks a year holiday? He could ask her for half of the summer holidays (3 weeks) and use more annual leave to enable him to be there for them. It seems she may well agree to that without any Court involvement.
Can you OH/you facilitate the children's school runs / after school clubs? I see 30 mins before and after school childcare as a negligible amount of time, especially if that time is spent with relatives from your OH's side of the family - it could be a nice benefit for the children popping in to see nanna and grandad after school on days with dad for example. What about school clubs? If you can't facilitate their normal routine (football on Wednesdays, Cubs on Thursdays etc) then their mum has a very valid argument.
As for not wanting him involved in school matters, that's not her choice. Ensure you OH speaks with the head teacher, print off and take in the contact order and birth certificates so they know he has parental Responsibility and perhaps also print off the relevant parts of the Education Act which states schools MUST communicate with non resident parents. He needs to ensure he gets copies of letters home, reports and has chance to attend parents evenings, school plays, performances, awards etc.
Could it be about money? If things are not friendly and your OH pays maintenance via the CSA the more nights they stay with him the less he is required to pay her...
Call a local family mediation company and invite the mum to mediate first though. Must cheaper and less stressful than Court and she may just have worries/concerns that your OH can easily relieve and they may come to an amicable decision. Then they can jointly apply to have the order changed by consent to reflect the new agreements.